Journal ArticleDOI
Three‐dimensional optimal perturbations in viscous shear flow
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In this paper, a complete set of perturbations, ordered by energy growth, is found using variational methods. But the optimal perturbation is not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbance to grow by as much as three orders of magnitude.Abstract:
Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made to understand this phenomena by finding the linear three‐dimensional perturbations that gain the most energy in a given time period. A complete set of perturbations, ordered by energy growth, is found using variational methods. The optimal perturbations are not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbation to grow by as much as three orders of magnitude. It is suggested that excitation of these perturbations facilitates transition from laminar to turbulent flow. The variational method used to find the optimal perturbations in a shear flow also allows construction of tight bounds on growth rate and determination of regions of absolute stability in which no perturbation growth is possible.read more
Citations
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Hydrodynamic Stability Without Eigenvalues
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Spectral Properties of Dynamical Systems, Model Reduction and Decompositions
TL;DR: Mezic and Banaszuk as mentioned in this paper applied spectral properties of the linear Koopman operator associated with the asymptotic dynamics on the attractor of a high-dimensional dynamical system to obtain a decomposition of the process.
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The MEMS Handbook
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Nonmodal Stability Theory
TL;DR: In this article, a general formulation based on the linear initial-value problem, circumventing the normal-mode approach, yields an efficient framework for stability calculations that is easily extendable to incorporate time-dependent flows, spatially varying configurations, stochastic influences, nonlinear effects, and flows in complex geometries.
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On a self-sustaining process in shear flows
TL;DR: In this article, a self-sustaining process for wall-bounded shear flows is investigated, which consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls.
References
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Numerical Recipes in C: The Art of Scientific Computing
TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
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Numerical Recipes, The Art of Scientific Computing
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Geophysical Fluid Dynamics
TL;DR: In this article, the authors propose a quasigeostrophic motion of a Stratified Fluid on a Sphere (SFL) on a sphere, which is based on an Inviscid Shallow-Water Theory.
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On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion
TL;DR: In this paper, the authors compare the results of a singular solution of Navier's equations of motion of viscous fluid with the results obtained from many experiments, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved.
Journal ArticleDOI
Accurate solution of the Orr–Sommerfeld stability equation
TL;DR: In this article, the Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm.